I graduated college in 3 years and I'm in my 4th year of higher education, but first year of graduate school. Do I qualify for the American Opportunity Credit?

Yes, Under the following conditions a student that has not completed the first four years of post-secondary education as of the beginning of the taxable year, and has not claimed the Hope scholarship credit and/or the American opportunity tax credit for more than four taxable years, the student can claim the American opportunity tax credit for qualified expenses paid during the entire taxable year.  Provided they meet the eligibility requirements below.

Eligibility requirements

A student eligible for the American Opportunity tax credit:

• Has not completed the first four years of post-secondary education.
• Enrolls in at least one academic semester during the applicable tax year.
• Maintains at least half-time status in a program leading to a degree or other credential.
• If the student has ever been a state or federal criminal because of a drug conviction, then he/she isn’t eligible for the tax credit. If a student has not completed the first four years of post-secondary education as of the beginning of the taxable year, and has not claimed the Hope scholarship credit and/or the American opportunity tax credit for more than four taxable years, the student can claim the American opportunity tax credit for qualified expenses paid during the entire taxable year.
• If the student has ever been a state or federal criminal because of a drug conviction, then he/she isn’t eligible for the tax credit. 

You can claim the American opportunity credit for only four tax years, and you can't claim it if you've finished your first four years of post-secondary school before the start of the year. However, this leaves open the possibility of using the American opportunity credit for your first semester of grad school if you graduated in the spring and started graduate school in the fall and if that tax year is no more than the fourth year you have claimed the credit. The advantage to claiming the American opportunity credit is that the $2,500 maximum credit is larger than the other tax breaks and up to 40 percent is refundable, which means that even if you don't owe any taxes, you'll get up to a $1,000 refund. The other advantage is you include the cost of books and other supplies when figuring the credit.

Graduate school's expensive, so any tax breaks you can drum up to offset your costs are always welcome. Generally, graduate students -- or those claiming them as a dependent -- won't be able to claim the American opportunity credit but will still be eligible for the tuition and fees deduction and the lifetime learning credit.